Hint
Use the stated units and precision. Calculate the rising-segment gradient.
Worked solution
(a)
Calculate the rising-segment gradient.
\(\displaystyle \frac{5}{2}\) is the speed increase divided by its time.
Answer: \(\displaystyle \frac{5}{2}\)
(b)
Distinguish the positive magnitude from the negative signed gradient.
\(5\) is the magnitude of the speed decrease divided by the braking time.
Answer: \(5\)
(c)
Add both half-base-times-height areas and the constant-speed rectangle.
Two triangle areas and the rectangle give \(70\) m.
Answer: \(70\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 2 marks
- 1 mark: Calculate the rising-segment gradient.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
(b) · 2 marks
- 1 mark: Distinguish the positive magnitude from the negative signed gradient.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Add both half-base-times-height areas and the constant-speed rectangle.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
Total: 6 marks.